Question

${\int }_{a+c}^{b+c}f\left(x\right)\mathrm{dx}$ is equal to

• A. ${\int }_a^{b}f(x-c)\mathrm{dx}$
• B. ${\int }_a^{b}f(x+c)\mathrm{dx}$
• C. ${\int }_a^{b}f\left(x\right)\mathrm{dx}$
• D. ${\int }_{a-c}^{b-c}f\left(x\right)\mathrm{dx}$

Answer 1

The correct option is B ${\int }_a^{b}f(x+c)\mathrm{dx}$

${\int }_{a+c}^{b+c}f\left(x\right)\mathrm{dx}$By putting x = t + c in the given expression, we get
${\int }_a^{b}f(t+c)\mathrm{dt}={\int }_a^{b}f(x+c)\mathrm{dx}$